Lemma 1 (Divergence Borel–Cantelli Lemma, [1]}) 
Suppose \((X, \mu )\)  is a finite measure space and \((A_q)_{q \in {N}} \subset X\)  is a
sequence of measurable subsets such that \(\sum \mu (A_q)=\infty \) . Then
\(\mu *{\limsup _{q\rightarrow \infty } A_q} \ge \limsup _{Q\rightarrow \infty } \frac{*{\sum _{q=1}^Q \mu (A_q)}^2}{\sum _{q,r=1}^Q\mu (A_q\cap A_r)}.\) 

